Motivated by the harmonic analysis of selfaffine measures, we introduce a class representations Cuntz algebra associated to random walks on graphs. The are constructed using dilation theory row coisometries. We study these representations, their commutant and intertwining operators.

Higher-rank graph generalisations of the Popescu-Poisson transform are constructed, allowing to obtain joint dilations of the families of operators satisfying certain commutation relations encoded by the graph structure. Several applications to the analysis of the structure of concrete graph operator algebras are presented. The starting point of classical dilation theory was the construction of...

We extend the notion of dilation distance to strongly continuous one-parameter unitary groups. If dilation distance between two such groups is finite, then these can be represented on same space in a way that their generators have domain and are fact bounded perturbation one another. This result extends <mml:math xmlns:mml="http://www...

We prove that non-self-adjoint harmonic and anharmonic oscillator operators have non-trivial pseudospectra. As a consequence, the computation of high energy resonances by the dilation analyticity technique is not numerically stable.

Edge detection plays a important role in image analysis. It is used to detect the different edges in the images. By using the combination of different morphological operators in the proposed method like erosion, dilation with the different edge operators like Robert ,prewitt, sobel, log and canny to find the edges by using the structure element. The fine edges in different direction can be dete...

We study multivariate trigonometric polynomials satisfying the “sum-rule” conditions of a certain order. Based on the polyphase representation of these polynomials relative to a general dilation matrix, we develop a simple constructive method for a special type of decomposition of such polynomials. These decompositions are of interest in the analysis of convergence and smoothness of multivariat...

We interpret the Central Limit Theorem as a fixed point theorem for a certain operator, and consider the problem of linearizing this operator. In classical as well as in free probability theory [VDN92], we consider two methods giving such a linearization, and interpret the result as a weak form of the CLT. In the classical case the analysis involves dilation operators; in the free case more gen...

We introduce a class of pseudodifferential operators in the anisotropic setting induced by an expansive dilation A which generalizes the classical isotropic class S γ,δ of inhomogeneous symbols. We extend a well-known L -boundedness result to the anisotropic class S δ,δ(A), 0 ≤ δ < 1. As a consequence, we deduce that operators with symbols in the anisotropic class S 1,0(A) are bounded on L p sp...